本文是实验设计与分析（第6版，Montgomery著，傅珏生译) 第3章单因子实验：方差分析3.11思考题3.7 R语言解题。主要涉及单因子方差分析，正态性假设检验，残差与拟合值的关系图，平方根变换。
X<-c(3,5,3,7,6,5,3,2,1,6,1,3,4,7,5,6,3,2,1,7,4,1,3,5,7,1,2,4,2,7,3,5,7,5,10,3,4,7,2,7)
A<-factor(rep(1:4,each=10))
miscellany<-data.frame(X,A)
aov.mis<-aov(X~A, data=miscellany)
summary(aov.mis)
> summary(aov.mis)
Df Sum Sq Mean Sq F value Pr(>F)
A 3 16.67 5.558 1.11 0.358
Residuals 36 180.30 5.008
TukeyHSD(aov.mis)
> TukeyHSD(aov.mis)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = X ~ A, data = miscellany)
$A
diff lwr upr p adj
2-1 -0.2 -2.8954706 2.495471 0.9971215
3-1 -0.5 -3.1954706 2.195471 0.9586389
4-1 1.2 -1.4954706 3.895471 0.6314346
3-2 -0.3 -2.9954706 2.395471 0.9904787
4-2 1.4 -1.2954706 4.095471 0.5082612
4-3 1.7 -0.9954706 4.395471 0.3392640
opar <- par(mfrow=c(2,2),cex=.8)
plot(aov.mis)
par(opar)
（c）
# 使用sqrt()函数进行平方根变换
sqrt_transformed_data <- sqrt(X)
print(sqrt_transformed_data)
miscellany<-data.frame(sqrt_transformed_data,A)
aov.mis<-aov(sqrt_transformed_data ~A, data=miscellany)
summary(aov.mis)
> summary(aov.mis)
Df Sum Sq Mean Sq F value Pr(>F)
A 3 1.087 0.3622 1.105 0.36
Residuals 36 11.807 0.3280
)
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